Problem: Simplify the following expression: $ t = \dfrac{-6x}{x - 10} + \dfrac{9}{10} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{10}{10}$ $ \dfrac{-6x}{x - 10} \times \dfrac{10}{10} = \dfrac{-60x}{10x - 100} $ Multiply the second expression by $\dfrac{x - 10}{x - 10}$ $ \dfrac{9}{10} \times \dfrac{x - 10}{x - 10} = \dfrac{9x - 90}{10x - 100} $ Therefore $ t = \dfrac{-60x}{10x - 100} + \dfrac{9x - 90}{10x - 100} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{-60x + 9x - 90}{10x - 100} $ $t = \dfrac{-51x - 90}{10x - 100}$